Browsing by Author "Akcengiz, Ziya"
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Article Citation Count: 0LS-14 test suite for long sequences(Hacettepe Univ, Fac Sci, 2024) Sulak, Fatih; Aslan, Melis; Doganaksoy, Ali; Sulak, Fatih; Uguz, Muhiddin; MathematicsRandom number sequences are used in many branches of science. Because of many technical reasons and their practicality, pseudo random sequences are usually employed in place of true number sequences. Whether a sequence generated through a deterministic process is a pseudo random, in other words, random-looking sequence or it contains certain patterns, can be determined with the help of statistics and mathematics. Although, in the literature there are many statistical randomness tests for this purpose, there is no much work on test suites specialized for long sequences, that is sequences of length 1,000,000 bits or more. Most of the randomness tests for long sequences use some mathematical approximations to compute expected values of the random variables and hence their results contain some errors. Another approach to evaluate randomness criteria of long sequences is to partition the long sequence into a collection short sequences and evaluate the collection for the ran- domness using statistical goodness of fit tests. The main advantage of this approach is, as the individual sequences are short, there is no need to use mathematical approximations. On the other hand when the second approach is preferred, partition the long sequence into a collection of fixed length subsequences and this approach causes a loss of information in some cases. Hence the idea of dynamic partition should be included to perform a more reliable test suite. In this paper, we propose three new tests, namely the entire R2 run, dynamic saturation point, and dynamic run tests. Moreover, we intro duce a new test suite, called LS-14, consisting of 14 tests to evaluate randomness of long sequences. As LS-14 employs all three approaches: testing the entire long sequence, testing the collection of fixed length partitions of it, and finally, testing the collection obtained by the dynamic partitions of it, the proposed LS-14 test suit differs from all existing suites. Mutual comparisons of all 14 tests in the LS-14 suite, with each other are computed. Moreover, results obtained from the proposed test suite and NIST SP800-22 suite are compared. Examples of sequences with certain patterns which are not observed by NIST SP800-22 suite but detected by the proposed test suite are given.Article Citation Count: 12Mutual correlation of NIST statistical randomness tests and comparison of their sensitivities on transformed sequences(Tubitak Scientific & Technological Research Council Turkey, 2017) Sulak, Fatih; Sulak, Fatih; Uguz, Muhiddin; Seker, Okan; Akcengiz, Ziya; MathematicsRandom sequences are widely used in many cryptographic applications and hence their generation is one of the main research areas in cryptography. Statistical randomness tests are introduced to detect the weaknesses or nonrandom characteristics that a sequence under consideration may have. In the literature, there exist various statistical randomness tests and test suites, defined as a collection of tests. An efficient test suite should consist of a number of uncorrelated statistical tests each of which measures randomness from another point of view. `Being uncorrelated' is not a well-defined or well-understood concept in the literature. In this work, we apply Pearson's correlation test to measure the correlation between the tests. In addition, we define five new methods for transforming a sequence. Our motivation is to detect those tests whose results are invariant under a certain transformation. To observe the correlation, we use two methods. One is the direct correlation between the tests and the other is the correlation between the results of a test on the sequence and its transformed form. In light of the observations, we conclude that some of the tests are correlated with each other. Furthermore, we conclude that in designing a reliable and efficient suite we can avoid overpopulating the list of test functions by employing transformations together with a reasonable number of statistical test functions.Article Citation Count: 0Mutual correlation of NIST statistical randomness tests and comparison of theirsensitivities on transformed sequences(2017) Sulak, Fatih; Sulak, Fatih; Uğuz, Muhiddin; Şeker, Okan; Akcengiz, Ziya; MathematicsRandom sequences are widely used in many cryptographic applications and hence their generation is oneof the main research areas in cryptography. Statistical randomness tests are introduced to detect the weaknesses ornonrandom characteristics that a sequence under consideration may have. In the literature, there exist various statisticalrandomness tests and test suites, de ned as a collection of tests. An efficient test suite should consist of a number ofuncorrelated statistical tests each of which measures randomness from another point of view. `Being uncorrelated\\' is nota well-de ned or well-understood concept in the literature. In this work, we apply Pearson\\'s correlation test to measurethe correlation between the tests.In addition, we de ne ve new methods for transforming a sequence. Our motivation is to detect those testswhose results are invariant under a certain transformation. To observe the correlation, we use two methods. One is thedirect correlation between the tests and the other is the correlation between the results of a test on the sequence andits transformed form. In light of the observations, we conclude that some of the tests are correlated with each other.Furthermore, we conclude that in designing a reliable and efficient suite we can avoid overpopulating the list of testfunctions by employing transformations together with a reasonable number of statistical test functions.Article Citation Count: 13New Statistical Randomness Tests Based on Length of Runs(Hindawi Ltd, 2015) Sulak, Fatih; Sulak, Fatih; Uguz, Muhiddin; Seker, Okan; Akcengiz, Ziya; MathematicsRandom sequences and random numbers constitute a necessary part of cryptography. Many cryptographic protocols depend on random values. Randomness is measured by statistical tests and hence security evaluation of a cryptographic algorithm deeply depends on statistical randomness tests. In this work we focus on statistical distributions of runs of lengths one, two, and three. Using these distributions we state three new statistical randomness tests. New tests use chi(2) distribution and, therefore, exact values of probabilities are needed. Probabilities associated runs of lengths one, two, and three are stated. Corresponding probabilities are divided into five subintervals of equal probabilities. Accordingly, three new statistical tests are defined and pseudocodes for these new statistical tests are given. New statistical tests are designed to detect the deviations in the number of runs of various lengths from a random sequence. Together with some other statistical tests, we analyse our tests' results on outputs of well-known encryption algorithms and on binary expansions of e, pi, and root 2. Experimental results show the performance and sensitivity of our tests.Conference Object Citation Count: 0Statistical Randomness Tests of Long Sequences by Dynamic Partitioning(Ieee, 2020) Sulak, Fatih; Asian, Melis; Karabayir, Ozgur; Doganaksoy, Ali; Uguz, Muhiddin; Sulak, Fatih; MathematicsRandom numbers have a wide usage in the area of cryptography. In practice, pseudo random number generators are used in place of true random number generators, as regeneration of them may be required. Therefore because of generation methods of pseudo random number sequences, statistical randomness tests have a vital importance. In this paper, a randomness test suite is specified for long binary sequences. In literature, there are many randomness tests and test suites. However, in most of them, to apply randomness test, long sequences are partitioned into a certain fixed length and the collection of short sequences obtained is evaluated instead. In this paper, instead of partitioning a long sequence into lixed length subsequences, a concept of dynamic partitioning is introduced in accordance with the random variable in consideration. Then statistical methods are applied. The suggested suite, containing four statistical tests: Collision Tests, Weight Test, Linear Complexity Test and Index Coincidence Test, all of them work with the idea of dynamic partitioning. Besides the adaptation of this approach to randomness tests, the index coincidence test is another contribution of this work. The distribution function and the application of all tests are given in the paper.